Question

Find the equation of the exponential function represented by the table below:
HELLPPP

Answer 1

y = 4 (\frac{1}{2}) ^{x}

Answer 2

y = 4
`((1)/(2)) ^(x)`

Explanation:

For an exponential function in the form

y = a
`b^(x)`

Use ordered pairs from the table to find values of a and b

Using (0, 4 ), then

4 = a
`b^(0)` (
`b^(0)` = 1 ), thus

a = 4, so

y = 4
`b^(x)`

Using (1, 2 ) , then

2 = 4
`b^(1)` = 4b ( divide both sides by 4 )

b =
`(1)/(2)`

Thus exponential function is

y = 4
`((1)/(2)) ^(x)`